Minimal scalar leptoquark model for $R_{D(*)}$

Motivated by the long-standing discrepancy in lepton flavor universality ratios $R_D$ and $R_{D^*}$ we assess the status of scalar leptoquark states $R_2$, $\tilde{R}_2$, and $S_1$ which can in principle provide a desired enhancement of $Br(B\rightarrow D^{(*)} \tau \nu)$ in a minimal setup with two Yukawa couplings only. We consider unavoidable low-energy constraints, $Z$-pole measurements as well as high-$p_T$ constraints. After setting mass of each leptoquark to $1.5$ TeV we find that of all considered states only $S_1$ leptoquark, coupled to both chiralities of leptons and quarks, is still a completely viable solution. On the other hand, the scenario with $R_2$ is in growing tension with $\Gamma(Z\rightarrow \tau\tau)$ and with the LHC constraints on the di-tau tails at high-$p_T$ while the $\tilde{R}_2$ scenario is excluded by the $Br(B\rightarrow K^{(*)} \nu\nu)$ observable. We comment on the future experimental tests of $S_1$ scenario. Furthermore, a scenario of the $S_1$ leptoquark coupled exclusively to right-handed SM fermions and a right-handed neutrino $N_R$ is also investigated as a potential solution for the $R_{D^{(*)}}$ with possible effects also in $Br(B\rightarrow K \nu \nu)$ .